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Proof step 24 from proof prepost-add-log-leb (previous step)

# buf3 = EB_PAGE_SIZE, m5 + # lpt = # avol, avol[m6] = mapped(buf1), avol[0] = mapped(buf2), avol[m2] = mapped(buf0), avol0 = avol, # buf1 ≠ LEB_SIZE, m6 < # avol, disk-layout(mksb(adr, m7, m6, m2, m3, m4, m5), # lpt), ebm-vol-inv(avol), is-encoded(log, buf1), is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m7, m6, m2, m3, m4, m5), buf2), is-encoded(rnode(m8), buf3), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)), # buf1 + EB_PAGE_SIZE ≤ LEB_SIZE ⊦ [ebm_avol_write#(m6, # buf1, 0, EB_PAGE_SIZE, buf3; avol; err)] ( ebm-vol-inv(avol) → ⟪logoff := # buf1; if err = ESUCCESS then logoff := logoff + EB_PAGE_SIZE else {logoff := LEB_SIZE; debug#("persistence-io: failed to add LEB " + m8.toString + " to log")}⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ subarray(avol, m5, # lpt) = subarray(avol0, m5, # lpt) ∧ ( err = ESUCCESS → m5 + # lpt = # avol ∧ avol[0].mapped? ∧ is-encoded(mksb(adr, m7, m6, m2, m3, m4, m5), avol[0].data) ∧ avol[m2].mapped? ∧ is-encoded-pad(orphans, m3, avol[m2].data) ∧ avol[m6].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m6].data = logoff) ∧ is-encoded(log + m8 ', avol[m6].data) ∧ mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)) ∧ is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE)))) ∧ ( err ≠ ESUCCESS → m5 + # lpt = # avol ∧ avol[0].mapped? ∧ is-encoded(mksb(adr, m7, m6, m2, m3, m4, m5), avol[0].data) ∧ avol[m2].mapped? ∧ is-encoded-pad(orphans, m3, avol[m2].data) ∧ avol[m6].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m6].data = logoff) ∧ is-encoded(log, avol[m6].data) ∧ mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)) ∧ is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE))))))

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 25:
# buf3 = EB_PAGE_SIZE, m5 + # lpt = # avol, avol[m2] = mapped(buf0), avol[0] = mapped(buf2), avol[m6] = mapped(buf1), avol0 = avol, buf = buf3, m = # buf1, m0 = m6, n0 = EB_PAGE_SIZE, n1 = 0, m6 < # avol, disk-layout(mksb(adr, m7, m6, m2, m3, m4, m5), # lpt), ebm-vol-inv(avol), is-encoded(rnode(m8), buf3), is-encoded(mksb(adr, m7, m6, m2, m3, m4, m5), buf2), is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)), # buf1 + EB_PAGE_SIZE ≤ LEB_SIZE ⊦ [if m0 < # avol ∧ avol[m0].mapped? ∧ # avol[m0].data ≤ m ∧ is-aligned(m, EB_PAGE_SIZE) ∧ is-aligned(n0, EB_PAGE_SIZE) ∧ m + n0 ≤ LEB_SIZE ∧ n1 + n0 ≤ # buf then {fail_or_success#(; ; err); if err = ESUCCESS then if n0 ≠ 0 then avol[m0] := mapped(avol[m0].data + mkempbuf(m - # avol[m0].data) + subarray(buf, n1, n0)) else choose n with n < n0 ∧ is-aligned(n, EB_PAGE_SIZE) in if n ≠ 0 then avol[m0] := mapped(avol[m0].data + mkempbuf(m - # avol[m0].data) + subarray(buf, n1, n)) ifnone skip} else abort] ( ebm-vol-inv(avol) → ⟪logoff := # buf1; if err = ESUCCESS then logoff := logoff + EB_PAGE_SIZE else {logoff := LEB_SIZE; debug#("persistence-io: failed to add LEB " + m8.toString + " to log")}⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ subarray(avol, m5, # lpt) = subarray(avol0, m5, # lpt) ∧ ( err = ESUCCESS → m5 + # lpt = # avol ∧ avol[0].mapped? ∧ is-encoded(mksb(adr, m7, m6, m2, m3, m4, m5), avol[0].data) ∧ avol[m2].mapped? ∧ is-encoded-pad(orphans, m3, avol[m2].data) ∧ avol[m6].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m6].data = logoff) ∧ is-encoded(log + m8 ', avol[m6].data) ∧ mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)) ∧ is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE)))) ∧ ( err ≠ ESUCCESS → m5 + # lpt = # avol ∧ avol[0].mapped? ∧ is-encoded(mksb(adr, m7, m6, m2, m3, m4, m5), avol[0].data) ∧ avol[m2].mapped? ∧ is-encoded-pad(orphans, m3, avol[m2].data) ∧ avol[m6].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m6].data = logoff) ∧ is-encoded(log, avol[m6].data) ∧ mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)) ∧ is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE)))))), # buf1 = LEB_SIZE

Rule argument

pos: right 1

Additional information

Used simplifier rules: ebm_avol_write#(LNUM, OFFSET, N0, N, BUF; AVOL; ERR) {if LNUM < # AVOL ∧ AVOL[LNUM].mapped? ∧ # AVOL[LNUM].data ≤ OFFSET ∧ is-aligned(OFFSET, EB_PAGE_SIZE) ∧ is-aligned(N, EB_PAGE_SIZE) ∧ OFFSET + N ≤ LEB_SIZE ∧ N0 + N ≤ # BUF then {fail_or_success#(; ; ERR); if ERR = ESUCCESS then if N ≠ 0 then AVOL[LNUM] := mapped ( AVOL[LNUM].data + mkempbuf(OFFSET - # AVOL[LNUM].data) + subarray(BUF, N0, N)) else choose N1 with N1 < N ∧ is-aligned(N1, EB_PAGE_SIZE) in if N1 ≠ 0 then AVOL[LNUM] := mapped ( AVOL[LNUM].data + mkempbuf(OFFSET - # AVOL[LNUM].data) + subarray(BUF, N0, N1)) ifnone skip} else abort };